I need to know what rights as a father do I have as far as visitation and custody over my child.

A biological father has the right to reasonable visitation. If you have not been to court, you can file a motion to establish paternity. Even if you are on the birth certificate you would need to do this to let the court know you are the father. The next step is to establish custody and a parenting schedule. Kentucky recognizes two forms of custody. I published a guide on Kentucky Divorce. I realize that you were not married to the mother but section 5 of the guide explains Custody, Parenting Schedule, and Child support (and they will apply to your situation). I have attached a link tot he guide below. I have also attached a link to the model timesharing/visitation guidelines. Keep in mind that this schedule is only a model and the court is not required to follow it. The Court is supposed to order a schedule that is in the best interest of the children so it may deviate from the model if it finds a deviation is in the child's best interest. Both custody and visitation decisions are based on the child's best interest so being able to pass a drug test, hold a job, and have a stable home are factors that will help your case. Lastly, if a child is under 4 than child support may be applied retroactively to the date of the child's birth. For this reason it is often better to set child support early (to avoid having the other parent request child support when the child is three and you instantly owing three years of back support). By filing early, you would know what your obligation would be each month. There are calculators online for you to determine what your child support would be under the Kentucky guidelines. You certainly have rights to see your child. I strongly advise you to retain an attorney to assist you with this matter. Best of luck.